1. Field of the Invention
The present invention relates to a statistical simulation method and corresponding simulation system for statistically computing an expected value of a physical quantity or the like, and a storing medium in which a statistical program is recorded. The present application claims priority under 35 U.S.C. .sctn.119 of Japanese Patent Application No. 9-082723, filed Apr. 1, 1997, the entire disclosure of which is incorporated herein by reference.
2. Description of the Related Art
The Monte Carlo method is well known as a statistical simulation method for statistically computing an expected value of a physical quantity or the like. This Monte Carlo method has been heretofore widely used in, for example, the device modeling field. TED ("Gunn Effect Device"), MOSFET, MESFET, bipolar transistors, hetero-structure devices, Schottky diodes, photo-detectors and the like are known as devices developed by the use of this method. It will be appreciated that the Monte Carlo method can also be used for simulation of PN junction devices, heterojunction devices, or the like. It will also be noted that the Monte Carlo method has applications to other many-body problems having numerous collected uncertainties, e.g., operations research and research in the sociology field.
It will be appreciated that the above-described Monte Carlo method is a method for computing or simulating a stochastic phenomenon by generating random numbers and constructing the stochastic phenomenon. As disclosed in U.S. Pat. No. 5,301,118, which reference is incorporated herein by reference, Monte Carlo analysis is a predictive technique, which can be used, for example, to determine variation of assemblies based on probabilistic modeling. Monte Carlo analysis is performed by establishing a range for each individual component tolerance, for example a range of USL-LSL expressed in terms of a probability density function. A random sampling fitting a mathematically defined distribution is taken from within this range, and the response of the circuit or system is evaluated. The output values can then be further analyzed using traditional statistical methods.
Monte Carlo analysis, i.e., analysis performed according to the Monte Carlo method, uses a random number generator to perform the distribution sampling. Therefore, it will be appreciated that Monte Carlo simulation can be employed to simulate large sample sizes on digital computers. In particular, Monte Carlo analysis is especially useful where complex assemblies can not be readily or realistically analyzed by traditional linear methods, such as root- sum- of -squares analysis or worst case analysis. It will also be appreciated that Monte Carlo analysis can be useful where the completed assemblies needing analysis are costly or time consuming to manufacture.
Assuming that this Monte Carlo method is applied to a many-particle simulation, this method is based on the assumption that a motion of a certain particle (an electron or a molecule) can be tracked over a sufficiently long time whereby information on the behavior of the whole electronic system or the entire gas system can be obtained. For example, in a free traveling process of a certain particle (carrier), an inherent stochastic distribution function can be used to establish conditions for determining the mean free path, whereby the random numbers are continuously generated. An elapse of time of the carrier is measured, whereby the motion of the particle is simulated.
The Monte Carlo method is based on the ergodic hypothesis that "a physical average is equal to a longtime average". That is, this method succeeds in using ergodicity of a deterministic equation (1) for generating the random numbers.